3,168 research outputs found
From Peierls brackets to a generalized Moyal bracket for type-I gauge theories
In the space-of-histories approach to gauge fields and their quantization,
the Maxwell, Yang--Mills and gravitational field are well known to share the
property of being type-I theories, i.e. Lie brackets of the vector fields which
leave the action functional invariant are linear combinations of such vector
fields, with coefficients of linear combination given by structure constants.
The corresponding gauge-field operator in the functional integral for the
in-out amplitude is an invertible second-order differential operator. For such
an operator, we consider advanced and retarded Green functions giving rise to a
Peierls bracket among group-invariant functionals. Our Peierls bracket is a
Poisson bracket on the space of all group-invariant functionals in two cases
only: either the gauge-fixing is arbitrary but the gauge fields lie on the
dynamical sub-space; or the gauge-fixing is a linear functional of gauge
fields, which are generic points of the space of histories. In both cases, the
resulting Peierls bracket is proved to be gauge-invariant by exploiting the
manifestly covariant formalism. Moreover, on quantization, a gauge-invariant
Moyal bracket is defined that reduces to i hbar times the Peierls bracket to
lowest order in hbar.Comment: 14 pages, Late
Evaluation of the InDUCKtion project at UCL
Executive summary: There is evidence that a good induction to university life can help with student retention; however, there is also a danger of overwhelming students during the intense period of fresher’s week. Under the auspices of a small grant from the Higher Education Academy’s ‘Changing the Learning Landscape’ funding stream, staff at two universities (University College London and Southampton Solent University) collaborated to produce an innovative and engaging induction project entitled ‘InDUCKtion’, based on the idea of an induction duck being a fun character for students to interact with. At UCL, the InDUCKtion duck existed in the form of a physical plastic duck included in international postgraduate student induction packs, and they were encouraged to take photos of themselves in and around UCL and London as part of a photo challenge using social media. It was anticipated that this would enable students to familiarise themselves with the locale, make friends and have fun at the same time. The InDUCKtion duck was also evident on flyers and posters with QR codes advertising an online tour to enable students to gain an accelerated familiarisation with the campus and its facilities. Within UCL, the project was a collaborative, cross-departmental venture instigated by members of UCL’s E-Learning Environments (ELE) working in partnership with the Centre for the Advancement of Learning and Teaching (CALT) and Student Support and Wellbeing (SSW). The logistics of the project meant that the team members also had to liaise with a number of other individuals and departments around UCL, to help promote and implement the project. Despite a rapid following on Twitter in a relatively short period, a reasonable hit rate on the QR code for the main page of the online tour resource, and some engagement with the photo challenges using social media, participation in the project was lower than anticipated. Lessons learned from an evaluation perspective revealed that adding another activity to an already overwhelming fresher’s week was problematic, despite its innovative and interactive nature. The use of QR codes was problematic for a number of reasons, and the project needed more buy-in from student representatives and academics to provide institutional endorsement. Recommendations for future instances of the project include securing student representation and academic endorsement, integrating the activity with parallel induction activities – particularly with academic departments, replacing QR codes with an alternative technology-enhanced learning approach and optimising the learning design to better motivate students and promote groupwork
A new antisymmetric bilinear map for type-I gauge theories
In the case of gauge theories, which are ruled by an infinite-dimensional
invariance group, various choices of antisymmetric bilinear maps on field
functionals are indeed available. This paper proves first that, within this
broad framework, the Peierls map (not yet the bracket) is a member of a larger
family. At that stage, restriction to gauge-invariant functionals of the
fields, with the associated Ward identities and geometric structure of the
space of histories, make it possible to prove that the new map is indeed a
Poisson bracket in the simple but relevant case of Maxwell theory. The building
blocks are available for gauge theories only: vector fields that leave the
action functional invariant; the invertible gauge-field operator, and the Green
function of the ghost operator.Comment: 10 page
Counter-term charges generate bulk symmetries
We further explore the counter-term subtraction definition of charges (e.g.,
energy) for classical gravitating theories in spacetimes of relevance to
gauge/gravity dualities; i.e., in asymptotically anti-de Sitter spaces and
their kin. In particular, we show in general that charges defined via the
counter-term subtraction method generate the desired asymptotic symmetries. As
a result, they can differ from any other such charges, such as those defined by
bulk spacetime-covariant techniques, only by a function of auxiliary
non-dynamical structures such as a choice of conformal frame at infinity (i.e.,
a function of the boundary fields alone). Our argument is based on the Peierls
bracket, and in the AdS context allows us to demonstrate the above result even
for asymptotic symmetries which generate only conformal symmetries of the
boundary (in the chosen conformal frame). We also generalize the counter-term
subtraction construction of charges to the case in which additional
non-vanishing boundary fields are present.Comment: 13 pages, Latex, no figures, v3: errors fixed, boundary terms
carefully controlled, awkward assumption removed, references update
DeWitt-Virasoro construction
We study a particular approach for analyzing worldsheet conformal invariance
for bosonic string propagating in a curved background using hamiltonian
formalism. We work in the Schrodinger picture of a single particle description
of the problem where the particle moves in an infinite-dimensional space.
Background independence is maintained in this approach by adopting DeWitt's
(Phys.Rev.85:653-661,1952) coordinate independent formulation of quantum
mechanics. This enables us to construct certain background independent notion
of Virasoro generators, called DeWitt-Virasoro (DWV) generators, and invariant
matrix elements of an arbitrary operator constructed out of them in spin-zero
representation. We show that the DWV algebra is given by the Witt algebra with
additional anomalous terms that vanish for Ricci-flat backgrounds. The actual
quantum Virasoro generators should be obtained by first introducing the vacuum
state and then normal ordering the DWV generators with respect to that. We
demonstrate the procedure in the simple cases of flat and pp-wave backgrounds.
This is a shorter version of arXiv:0912.3987 [hep-th] with many technical
derivations omitted.Comment: 18 pages, shorter version of arXiv:0912.3987 [hep-th] accepted for
publication in Pramana - Journal of Physic
Numerical modeling of runback water on ice protected aircraft surfaces
A numerical simulation for 'running wet' aircraft anti-icing systems is developed. The model includes breakup of the water film, which exists in regions of direct impingement, into individual rivulets. The wetness factor distribution resulting from the film breakup and the rivulet configuration on the surface are predicted in the numerical solution procedure. The solid wall is modeled as a multilayer structure and the anti-icing system used is of the thermal type utilizing hot air and/or electrical heating elements embedded with the layers. Details of the calculation procedure and the methods used are presented
A universal constraint between charge and rotation rate for degenerate black holes surrounded by matter
We consider stationary, axially and equatorially symmetric systems consisting
of a central rotating and charged degenerate black hole and surrounding matter.
We show that always holds provided that a continuous sequence of
spacetimes can be identified, leading from the Kerr-Newman solution in
electrovacuum to the solution in question. The quantity is the black
hole's intrinsic angular momentum per unit mass, its electric charge and
the well known black hole mass parameter introduced by Christodoulou and
Ruffini.Comment: 19 pages, 2 figures, replaced with published versio
Factor ordering in standard quantum cosmology
The Wheeler-DeWitt equation of Friedmann models with a massless quantum field
is formulated with arbitrary factor ordering of the Hamiltonian constraint
operator. A scalar product of wave functions is constructed, giving rise to a
probability interpretation and making comparison with the classical solution
possible. In general the bahaviour of the wave function of the model depends on
a critical energy of the matter field, which, in turn, depends on the chosen
factor ordering. By certain choices of the ordering the critical energy can be
pushed down to zero.Comment: 15 pages, 3 figure
Regularity of Cauchy horizons in S2xS1 Gowdy spacetimes
We study general S2xS1 Gowdy models with a regular past Cauchy horizon and
prove that a second (future) Cauchy horizon exists, provided that a particular
conserved quantity is not zero. We derive an explicit expression for the
metric form on the future Cauchy horizon in terms of the initial data on the
past horizon and conclude the universal relation A\p A\f=(8\pi J)^2 where
A\p and A\f are the areas of past and future Cauchy horizon respectively.Comment: 17 pages, 1 figur
Combustion of solid carbon rods in zero and normal gravity
In order to investigate the mechanism of carbon combustion, spectroscopic carbon rods were resistance ignited and burned in an oxygen environment in normal and zero gravity. Direct mass spectrometric sampling was used in the normal gravity tests to obtain concentration profiles of CO2, CO, and O2 as a function of distance from the carbon surface. The experimental concentrations were compared to those predicted by a stagnant film model. Zero gravity droptower tests were conducted in order to assess the effect of convection on the normal gravity combustion process. The ratio of flame diameter to rod diameter as a function of time for oxygen pressures of 5, 10, 15, and 20 psia was obtained for three different diameter rods. It was found that this ratio was inversely proportional to both the oxygen pressure and the rod diameter
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